Question

An exponential function is graphed on the grid

based on the graph, which statement about the function is true

a) the domain is the set of all real numbers

b) the domain is the set of all real numbers less than 3

c) the range is the set of all real numbers greater than or equal to 0

d) the range is the set of all real numbers greater than or equal to -9

Answer 1

a) the domain is the set of all real numbers

Explanation:

Given:

An exponential function and its graph.

A line parallel to
`x` axis is drawn at
`y=-9` which is a dashed line.

Dashed line means, the function does not attain a value equal to
`y=-9`.

Domain of a function,
`y=f(x)` is the set of values which can be possible for the variable
`x` that can be given as input.

Range of a function,
`y=f(x)` is the set of possible values of
`y` i.e. the output of the function.

As seen from the graph, the domain of the exponential function does not have any constraint on it.

Therefore, any real number can be given as input.

So, a) The domain is the set of all real numbers.

Let us discuss about the range of function.

As stated above as well, the range of the function can not contain the value
`y=-9`.

And there is no value possible below it.

So, the range is all real numbers greater than -9.

The answer is:

"a) the domain is the set of all real numbers" is true.